Tegmark Multiverse levels (idea)

The Swedish cosmologist Max Tegmark has postulated four different types, or levels, of multi-verse. These are:

Level 1:

The least controversial type of multi-verse, where parallel universes are simply beyond the cosmic event horizon. The cosmic event horizon grows at one light year per year, so, in principle, everything in parallel universes would eventually be visible. unfortunately for this, our species would most likely die out first.

In this model, people in other universes would experience the same physics, but have different starting conditions.

Level 2:

Inflation allows a slightly more elaborate multi-verse: the idea that our level 1 multi-verse is embedded in an even larger, or possibly infinitespace. This space would contain other parallel type 1 multi-verses, but is mostly empty.

Inflation implies that the vast majority of space will expand indefinitely, possibly faster that light, as the expansion of space is not limited by light speed. However, in some regions the inflation field will spontaneously drop away, and these regions form type 1 multi-verse bubbles, filled with matter formed from the energy from the inflation field.

Such bubbles would differ in not just initial conditions, but some "constants" in physical law. This is allowed because, based on what we know, physical constants are set early in the formation of the universe, via a process known as symmetry breaking.

Level 3:

Quantum many worlds interpretation. Every time a quantum superposition forms (e.g. Schroedinger's cat), it can be represented as a "blob" in the phase space of all possible universes. As the superposition expands (a human looking in the box) the parts of the blob that contain the different states (cat is alive, cat is exploded) separate more, forming different universes.

Level 4:

In the other levels of multi-verse, the initial conditions change, as do some fundamental constants, but the basic laws remain the same. In a level 4 multi-verse, this is not so. in fact a level 4 multi-verse contains every self consistent mathematical structure, including itself.

The way this works, at least in part, can be shown like this: a computer is a number of particles that perform calculations, but the way the particles are interpreted to form calculations is arbitrary. Given a set of particles, you can interpret there state, and the way they move between states, as any of a large number of calculations, and the number would seem to go up exponentially with the number of particles, although some of these will be equivalent. This shows that our universe is vast calculation an even larger number of smaller universes, however, by Occam's razor, we should not think we are at the top of this stack. In fact, since the number of possible mathematical objects increase as the maximum size increases, we are almost certainly near the bottom, and the stack may even be infinitely high.